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PERTANYAAN :

Jika p equals 16q equals 27 dan r equals 36, nilai dari fraction numerator p q to the power of negative begin display style 2 over 3 end style end exponent r to the power of negative begin display style 1 fourth end style end exponent over denominator p to the power of begin display style 1 half end style end exponent q to the power of negative 1 end exponent r to the power of negative begin display style 3 over 4 end style end exponent end fraction adalah …

Jawaban

hasil dari fraction numerator p q to the power of negative begin display style 2 over 3 end style end exponent r to the power of negative begin display style 1 fourth end style end exponent over denominator p to the power of begin display style 1 half end style end exponent q to the power of negative 1 end exponent r to the power of negative begin display style 3 over 4 end style end exponent end fraction equals 72.


Pembahasan

Substitusi nilai p equals 16q equals 27 dan r equals 36 pada fraction numerator p q to the power of negative begin display style 2 over 3 end style end exponent r to the power of negative begin display style 1 fourth end style end exponent over denominator p to the power of begin display style 1 half end style end exponent q to the power of negative 1 end exponent r to the power of negative begin display style 3 over 4 end style end exponent end fraction diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator p q to the power of negative begin display style 2 over 3 end style end exponent r to the power of negative begin display style 1 fourth end style end exponent over denominator p to the power of begin display style 1 half end style end exponent q to the power of negative 1 end exponent r to the power of negative begin display style 3 over 4 end style end exponent end fraction end cell equals cell fraction numerator left parenthesis 16 right parenthesis left parenthesis 27 right parenthesis to the power of negative begin display style 2 over 3 end style end exponent left parenthesis 36 right parenthesis to the power of negative begin display style 1 fourth end style end exponent over denominator left parenthesis 16 right parenthesis to the power of begin display style 1 half end style end exponent left parenthesis 27 right parenthesis to the power of negative 1 end exponent left parenthesis 36 right parenthesis to the power of negative begin display style 3 over 4 end style end exponent end fraction end cell end table

Ingat sifat-sifat bilangan berpangkat berikut:

  • a to the power of m over a to the power of n equals a to the power of m minus n end exponent space 
  • open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent 

Sehingga diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator p q to the power of negative begin display style 2 over 3 end style end exponent r to the power of negative begin display style 1 fourth end style end exponent over denominator p to the power of begin display style 1 half end style end exponent q to the power of negative 1 end exponent r to the power of negative begin display style 3 over 4 end style end exponent end fraction end cell equals cell fraction numerator left parenthesis 16 right parenthesis left parenthesis 27 right parenthesis to the power of negative begin display style 2 over 3 end style end exponent left parenthesis 36 right parenthesis to the power of negative begin display style 1 fourth end style end exponent over denominator left parenthesis 16 right parenthesis to the power of begin display style 1 half end style end exponent left parenthesis 27 right parenthesis to the power of negative 1 end exponent left parenthesis 36 right parenthesis to the power of negative begin display style 3 over 4 end style end exponent end fraction end cell row blank equals cell left parenthesis 16 right parenthesis to the power of 1 minus 1 half end exponent left parenthesis 27 right parenthesis to the power of negative 2 over 3 minus left parenthesis negative 1 right parenthesis end exponent left parenthesis 36 right parenthesis to the power of negative 1 fourth minus open parentheses negative 3 over 4 close parentheses end exponent end cell row blank equals cell left parenthesis 16 right parenthesis to the power of 1 half end exponent left parenthesis 27 right parenthesis to the power of negative 2 over 3 plus 3 over 3 end exponent left parenthesis 36 right parenthesis to the power of 2 over 4 end exponent end cell row blank equals cell left parenthesis 16 right parenthesis to the power of 1 half end exponent left parenthesis 27 right parenthesis to the power of 1 third end exponent left parenthesis 36 right parenthesis to the power of 1 half end exponent end cell row blank equals cell open parentheses 4 squared close parentheses to the power of 1 half end exponent open parentheses 3 cubed close parentheses to the power of 1 third end exponent open parentheses 6 squared close parentheses to the power of 1 half end exponent end cell row blank equals cell left parenthesis 4 right parenthesis left parenthesis 3 right parenthesis left parenthesis 6 right parenthesis end cell row blank equals 72 end table 

Dengan demikian, hasil dari fraction numerator p q to the power of negative begin display style 2 over 3 end style end exponent r to the power of negative begin display style 1 fourth end style end exponent over denominator p to the power of begin display style 1 half end style end exponent q to the power of negative 1 end exponent r to the power of negative begin display style 3 over 4 end style end exponent end fraction equals 72.


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